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Kth Smallest Number in Multiplication Table

Nearly everyone has used the Multiplication Table.

Nearly everyone has used the Multiplication Table. The multiplication table of size m x n is an integer matrix mat where mat[i][j] == i * j (1-indexed).

Given three integers m, n, and k, return the kth smallest element in the m x n multiplication table.

Example 1

Input: m = 3, n = 3, k = 5

Output: 3

Explanation: The 5th smallest number is 3.

Example 2

Input: m = 2, n = 3, k = 6

Output: 6

Explanation: The 6th smallest number is 6.

Constraints

  • 1 <= m, n <= 3 * 10^4
  • 1 <= k <= m * n

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